You have to know that the graph of the arctangent function is a flat S-shaped curve that goes through (0, 0) and has asymptotes at ±π/2. The factor of 2 that multiplies it here expands it vertically so the asymptotes are at ±π. The +3 added to the x causes it to be shifted to the left by 3 units.
440 gallons of 80 % antifreeze solution must be mixed with 80 gallons of 15% antifreeze to get a mixture that is 70% antifreeze
<em><u>Solution:</u></em>
Let "x" be the gallons of 80 % antifreeze added
Therefore, "x" gallons of 80 % antifreeze solution must be mixed with 80 gallons of 15% antifreeze
Final mixture is x + 80
Therefore, we can frame a equation as:
"x" gallons of 80 % antifreeze solution must be mixed with 80 gallons of 15% antifreeze to get (x + 80) gallons of 70 % antifreeze
Thus, we get,
x gallons of 80 % + 80 gallons of 15 % = (x + 80) gallons of 70 %
Thus 440 gallons of 80 % antifreeze solution must be mixed